The protest came a day after reports accused Prime Minister Sigmundur David Gunnlaugsson, who has led the country since 2013, of having ties to an offshore company that were not properly disclosed. Gunnlaugsson has denied the accusation.

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Photos:Panama Papers: People take to the streets in Iceland

The reports draw on millions of documents hacked from Mossack Fonseca, a Panamanian law firm that allegedly helped elected leaders and top officials set up secret shell companies and offshore accounts. Details from the leaked documents, which CNN hasn't been able to verify independently, drew fierce criticism from demonstrators Monday. "Man who lies should not be a leader of a nation," one protester's sign read.

As opposition lawmakers are pushing for a vote of no confidence in the prime minister, some protesters say they want him to step down. Gunnlaugsson has vowed to stay in office.

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Photos:Panama Papers: People take to the streets in Iceland

"I'm so angry I made a sign," one demonstrator's sign said.

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Photos:Panama Papers: People take to the streets in Iceland

Some protesters waved Iceland's flag as they marched.

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Photos:Panama Papers: People take to the streets in Iceland

Angry demonstrators said they felt betrayed by the prime minister. Gunnlaugsson told Iceland's TV2 Monday that he won't step down. "I have not considered resigning, nor am I going to resign, because of this matter," he said.